Problem: Rewrite as a simplified fraction. ${0.2\overline{7} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 27.7777...\\ 10x &= 2.7777...\end{align*}}$ Subtracting the two equations, we have: ${90x = 25}$ ${x = \dfrac{25}{90}} $ ${x = \dfrac{5}{18}} $